| Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
| 392.1-c3 |
392.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
392.1 |
\( 2^{3} \cdot 7^{2} \) |
\( 2^{10} \cdot 7^{4} \) |
$1.12462$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$7.189921948$ |
1.271010641 |
\( \frac{3543122}{49} \) |
\( \bigl[a\) , \( -1\) , \( a\) , \( -11\) , \( -11\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-11{x}-11$ |
| 784.1-c3 |
784.1-c |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
784.1 |
\( 2^{4} \cdot 7^{2} \) |
\( 2^{10} \cdot 7^{4} \) |
$1.33740$ |
$(a), (-2a+1), (2a+1)$ |
$1$ |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$0.119959949$ |
$22.75712104$ |
1.930361270 |
\( \frac{3543122}{49} \) |
\( \bigl[a\) , \( 0\) , \( a\) , \( -11\) , \( 10\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-11{x}+10$ |
| 2744.1-i3 |
2744.1-i |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2744.1 |
\( 2^{3} \cdot 7^{3} \) |
\( 2^{10} \cdot 7^{10} \) |
$1.82928$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$4.834724458$ |
1.709333224 |
\( \frac{3543122}{49} \) |
\( \bigl[a\) , \( a\) , \( a\) , \( -40 a - 91\) , \( 231 a + 262\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-40a-91\right){x}+231a+262$ |
| 2744.2-i3 |
2744.2-i |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2744.2 |
\( 2^{3} \cdot 7^{3} \) |
\( 2^{10} \cdot 7^{10} \) |
$1.82928$ |
$(a), (-2a+1), (2a+1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{4} \) |
$1$ |
$4.834724458$ |
1.709333224 |
\( \frac{3543122}{49} \) |
\( \bigl[a\) , \( -a\) , \( a\) , \( 40 a - 91\) , \( -231 a + 262\bigr] \) |
${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(40a-91\right){x}-231a+262$ |
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*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.
